Question 746845
if you mean find a polynomial of degree 6 with those zeros then here goes...



the general form would be:

{{{
P=a(x-(-4))(x-6)(x-(4-5i))(x-(4+5i))(x-(-6+i))(x-(-6-i)))
}}}


which after some work we get:
{{{
P=a(-6+x) (4+x) (41-8 x+x^2) (37+12 x+x^2)
}}}

and the principal polynomial is:



{{{
P=x^6+2 x^5-50 x^4+136 x^3+1557 x^2-7738 x-36408
}}}